If I want to plant another tree in EXACT same spot ....will I be able to grind down enough to eliminate stump and its tap roots completely?
Some trees have shallow roots, such as evergreens. Those stumps are much easier to remove. It helps to saturate the soil with water - it makes everything looser. Other trees, such as oaks and beeches, have very extensive root systems. If you're not in a hurry, the stump can be treated with acid (I think phosphoric acid works well for this). However, this method takes months.
I'd just grind down level and see if I could find a spot to plant the new tree. Dead roots will rot away and become organic matter to feed the new tree.
take your wedge and maul to the stump -- break it into pieces. you'll soon be able to pull some of the pieces out and can then see what's going on